Will academic dishonesty affect my transfer?

Hi,
I was just accused and claimed responsible for academic dishonesty. I've learned my mistakes, and I accepted my punishment. It's a year of probation, and of course a mark on my transcript. I can get the mark removed a year from now. But, I'm graduating next May, with hopes to return for two more bachelors degrees, and then to apply to vet school. I was hoping to move states to continue my undergrad education. Does my academic dishonesty affect my chances of moving schools? Or can I just wait to remove the mark, and then apply during the summer? I'd like to return the fall after I graduate.
Thanks for any advice.